We show that it is impossible to determine the time a tunneling particle spends under the barrier. However, it is possible to determine the asymptotic time, i.e., the time the particle spends in a large area including the barrier. We propose a model of time measurements. The model provides a procedure for calculation of the asymptotic tunneling and reflection times. The model also demonstrates the impossibility of the determination of the time the tunneling particle spends under the barrier. Examples for δ form and rectangular barrier illustrate the obtained results.

We analyze the coherence properties of polarized neutrons, after they have interacted with a magnetic field or a phase shifter undergoing different kinds of statistical fluctuations. We endeavor to probe the degree of disorder of the distribution of the phase shifts by means of the loss of quantum-mechanical coherence of the neutron. We find that the notion of entropy of the shifts and that of decoherence of the neutron do not necessarily agree. In some cases the neutron wave function is more coherent, even though it has interacted with a more disordered medium.

The desired interference required for quantum computing may be modified by wave-function oscillations for the implementation of quantum algorithms [Phys. Rev. Lett. 84, 1615 (2000)]. To diminish such a detrimental effect, we propose a scheme with trapped ion pairs as qubits and apply the scheme to the Grover search. It will be shown that our scheme cannot only carry out a full Grover search, but can also meet the requirement for scalable hot-ion quantum computing. Moreover, the ion-pair qubits in our scheme are more robust against decoherence and the dissipation caused by the environment than single-particle qubits proposed before.

For a system of N spins there are quantum states that can encode a direction in an intrinsic way. Information on this direction can later be decoded by means of a quantum measurement. We present here the optimal encoding and decoding procedure using the fidelity as a figure of merit. We compute the maximal fidelity and prove that it is directly related to the largest zeros of the Legendre and Jacobi polynomials. We show that this maximal fidelity approaches unity quadratically in $1/N.$ We also discuss this result in terms of the dimension of the encoding Hilbert space.

A multichannel quantum-defect theory (MQDT) is employed to obtain expressions for nonadiabatic coupling matrix elements without recourse to knowledge of the electronic wave functions. Diagonal and nondiagonal analogs of the Hellmann-Feynman theorem are derived by a differentiation of the MQDT quantization equations with respect to internuclear distance R. Closed relations for both the adiabatic correction terms and the nonadiabatic matrix elements are given in terms of nuclear derivatives of the reactance matrix. The theory is tested by calculating the adiabatic correction and nonadiabatic radial and angular coupling matrix elements for the ${g,h}^3{\Sigma }_g^{+}$ and ${4s,4d}^3{\Sigma }_g^{+}$ states, corresponding to the first members $(n=3\mathrm{}$ and 4) of the ${s,d}^3{\Sigma }_g^{+}$ Rydberg complex of the ${\mathrm{H}}_2$ molecule. The derived estimates agree well with available ab initio results.

Nuclear spin-state mixing affects magnetic resonance and relaxation, thereby providing means to obtain information about molecular and electronic structure and, through spin polarization of nuclear targets, nucleon structure. In this report a calculation of matrix elements of the intramolecular nuclear spin-state mixing Hamiltonian is formulated and carried out for the proton (deuteron) and ${}^{14}\mathrm{N}$ ${(}^{15}\mathrm{N})$ nuclei in isotopes of the small free radical ${\mathrm{NH}}_2.$ Two models of the electronic structure of the free radical are treated, one with the unpaired spin in a Slater orbital and the other employing an unrestricted Hartree-Fock basis set ${(6-31\mathrm{G}}^{\mathrm{*}}$ orbitals). With these matrix elements, the energies and spin-state mixing of the nuclear levels are quantified. For all four nuclei, the Slater matrix elements produce 23% smaller nuclear spin-state mixing than do the ${6-31\mathrm{G}}^{\mathrm{*}}$ elements. The Slater results are presented graphically. In the regions of magnetic-field strength where the energy separation of the hyperfine levels is least, mixing of the nuclear spin states is qualitatively different. In this “crossover” region unusual paths for both transverse and longitudinal nuclear spin polarization appear.

Recent experiments [E. M. Spain et al., J. Chem. Phys 102, 24 (1995)] discovered alignment effects in cross sections for near-resonant energy-transfer collisions of Xe atoms with Ca Rydberg atoms at a single mean relative velocity. A collaborative quantum-mechanical study [W. Isaacs and M. A. Morrison, Phys. Rev. A 57, R9 (1998)] confirmed these findings and discovered pronounced oscillations in the velocity dependence of state-to-state cross sections. Collisions corresponding to the ${17d}_{m_0}\to {18p}_m$ transitions in the Ca-He system are here analyzed semiclassically. This analysis shows that the origin of these oscillations is a phase interference process unique to Rydberg target states. We further demonstrate the importance of retaining the energy defect and of using quantum-defect phase-shifted radial functions in calculations of alignment cross sections for Rydberg states.

Charge-transfer collisions between slow multiply charged ions and highly excited Rydberg atoms have been studied to determine the details of the internal energy transfer accompanying charge exchange. The experiment uses lasers to define uniquely the binding energies of both initial and final states of the collision, thereby eliminating the ambiguity inherent in the selective field ionization method used for previous studies. The results clearly characterize the capture energetics over the range of ion charge $q=1\mathrm{}–11$ and velocity $v=0.031\mathrm{}–0.138\mathrm{a}.\mathrm{u}.\mathrm{}$ The measurements are in very good agreement with predictions of the classical trajectory Monte Carlo method, but not with predictions of other classical models.

A procedure for treating excitation of ions to specific magnetic sublevels by an electron beam is modified to apply for ionization. This is then used in the study of the linear polarization of the three x-ray lines ${(2p}^5{3s)}_{1,2}\to {(2p}^6{)}_0$ emitted by ${\mathrm{Se}}^{24+}.$ We do this by including population of the upper levels by innershell ionization of Na-like Se in addition to excitation from the ${(2p}^6{)}_0$ ground level of Ne-like Se both directly and via cascades from higher $n=3\mathrm{}$ levels. The required cross sections for both excitation and ionization to individual magnetic sublevels were computed in a fully relativistic distorted-wave method at impact energies ranging from 190 to 800 Ry. The radiative branching ratios were calculated using the fully relativistic GRASP atomic structure code. It is found that the innershell ionization process is almost unselective in populating the different $|M|$ sublevels of each upper level. Small values of the polarization degrees are obtained due to the combined effects of radiative cascades and inner-shell ionization.

The collisional stability of ultracold polar molecules in electrostatic traps is considered. Rate constants for collisions that drive molecules from weak-electric-field-seeking to strong-field-seeking states are estimated using a simple model that emphasizes long-range dipolar forces. The rate constants for collisional losses are found to vary substantially as a function of molecular parameters used in the model, such as dipole moment, mass, and the splitting of the molecular $\Lambda$ doublet. Varying these parameters over physically reasonable ranges yields rate constants as low as ${10}^{-20}\hspace{0.5em}{\mathrm{cm}}^3/\sec$ and as high as ${10}^{-10}\hspace{0.5em}{\mathrm{cm}}^3/\sec .$ Nevertheless, the loss rates rise dramatically in the presence of the externally applied trapping electric field. For this reason it is argued that electrostatic traps are likely to be less stable against collisional losses than their magnetic counterparts.

Using a crossed-beam method, we have measured absolute differential cross sections for the excitation of atomic hydrogen to its $n=2(2\mathrm{}{}^{2}S+2\mathrm{}{}^{2}P)$ level by electron impact. The angular range covered was from 12° to 156° in 12° increments, while the impact energies treated were 15, 20, 30, and 40 eV. Absolute integrated excitation cross sections were calculated from the differential ones. Agreement of our data with other recent data and calculations is quite good, but there are still some discrepancies among our results and the older data.

Collisional electron detachment of anions with ${\mathrm{np}}^3$ structures $(n=2,3,$ and 4), namely, ${\mathrm{C}}^{-},$ ${\mathrm{Si}}^{-},$ and ${\mathrm{Ge}}^{-},$ was studied for He, Ne, and Ar targets and relative velocities ranging from 0.2 a.u. to 2.2 a.u.. Single, double, and triple electron ejection cross sections were also measured for the ${\mathrm{C}}^{-}$ anion colliding with an Ar target, being observed to obey a binomial distribution. Two striking universal features were observed concerning the total detachment cross sections: for each target a multiplicative scaling may be made for the cross sections of the three projectiles, and these factors are target independent. The maxima of these three curves show a nonmonotonic correspondence with the noble-gas atomic numbers. A simple law, proposed for the scaling, indicates the presence of metastable states in the ${\mathrm{Si}}^{-}$ and ${\mathrm{Ge}}^{-}$ beams.

A theoretical model is developed to study the energy loss of heavy ions specularly reflected on a solid surface at a glancing angle using the dielectric response theory and the specular reflection model. A local-field correction and a plasmon-pole approximation for dielectric function are employed in the low- and high-velocity regimes, respectively. Also, the Brandt-Kitagawa model is used to express the distribution of the electrons bound to the projectiles. We obtain analytical expressions for the position-dependent stopping power and the surface image potential. The energy losses, dependent on the charge state of the ions and the incident angles, are calculated and compared with the corresponding experimental results.

The stopping power of swift heavy ions in both cold and plasma targets is expressed by a single formula from which the standard classical or quantum results are retrieved as specific limits. It is based on a modified Bloch correction term devoted to correctly describe the close collisions contribution to the energy-loss process. This correction term is deduced from the convergent kinetic theory (CKT) derived by Gould and DeWitt for calculating transport coefficients in dense plasmas. The CKT is adapted to neutral targets by using the scaling properties of Yukawa potentials demonstrated by Lindhard. The resulting CKLT stopping expression can be applied to partially ionized heavy ions with a non-Coulomb electron-ion interaction potential. The differences between the CKLT and standard stopping models are investigated in the binary approximation, where the CKLT formula yields the exact result. The usefulness of the CKLT procedure in stopping power applications is then demonstrated using the spherical harmonic oscillator as a target model. The validity domain of the CKLT is analyzed by comparing the results derived by adding the close collision correction term either to the Born I result or to a classical calculation. The classical result is obtained by following during a collision, the time evolution of the Wigner distribution.

We present a nonperturbative theoretical approach, based on Coulomb-Volkov-type states, which is able to predict both angular and energy distributions of ejected electrons when atoms interact with a very short and intense laser pulse. In a previous paper [Eur. Phys. J. D 11, 191 (2000)], it was shown that, for atomic hydrogen targets, this theory makes accurate predictions as long as the interaction time does not allow more than two optical cycles. Recently, multigigawatt laser pulses with a full width at half maximum of less than two optical cycles have been generated by Nisoli et al. [Opt. Lett. 22, 522 (1997)] at $\lambda =800\mathrm{}\mathrm{nm}.$ In the present paper, it is shown that predictions of the Coulomb-Volkov approach for the ionization of a hydrogen atom by laser pulses similar to the ones generated by Nisoli et al. are in very good agreement with the predictions of an “exact” numerical treatment. Further, the domain where the Coulomb-Volkov theory applies is marked out by means of a consistent accuracy parameter and by comparison with an “exact” numerical treatment. It is shown that, subject to the above-mentioned condition, good predictions may always be issued as long as the interaction time does not exceed half the initial orbital period of the electron. For a given laser pulse duration, predictions are all the better that the laser field amplitude is high and the initial quantum number is large.

A considerable number of higher-angular-momentum states of the helium atom embedded in a magnetic field $B=0\mathrm{}-100\mathrm{a}.\mathrm{u}.\mathrm{}$ are investigated using a full configuration-interaction approach which is based on a nonlinearly optimized anisotropic Gaussian basis set of one-particle functions. Spin singlet and triplet states with positive- and negative-z parity are considered for the magnetic quantum number $M=\pm 2$ and positive-z parity states are studied for $M=\pm 3.$ Many of the excitations within these symmetries are investigated here. Total energies, ionization energies, as well as transition wavelengths as a function of the field strength are given. A list of stationarities with respect to the field strength which are of immediate interest to astrophysical applications is available.

We study the competition between phase definition and quantum phase fluctuations in interference experiments between independently formed Bose condensates. While phase-sensitive detection of atoms makes the phase progressively better defined, interactions tend to randomize it faster as the uncertainty in the relative particle number grows. A steady state is reached when the two effects cancel each other. Then the phase resolution saturates to a value that grows with the ratio between the interaction strength and the atom detection rate, and the average phase and number begin to fluctuate classically. We discuss how our study applies to both recently performed and possible future experiments.

We utilize a two-gas model to simulate collective oscillations of a Bose-Einstein condensate at finite temperatures. The condensate is described using a generalized Gross-Pitaevskii equation, which is coupled to a thermal cloud modeled by a Monte Carlo algorithm. This allows us to include the collective dynamics of both the condensed and noncondensed components self-consistently. We simulate quadrupolar excitations, and measure the damping rate and frequency as a function of temperature. We also observe revivals in condensate oscillations at high temperatures, and in the thermal cloud at low temperature. Extensions of the model to include nonequilibrium effects and describe more complex phenomena are discussed.

We analyze the dynamical properties of arrays of coupled solid-state lasers. The interaction mechanism, valid in the weak-coupling limit, is local and described by a complex coupling parameter. We focus our attention on the possible synchronization or self-organization properties of the system. Besides the well-known phase of total order corresponding to complete locking, weaker collective order is observed and related to the formation of clusters of synchronized units. We discuss, in particular, the roles played in the existence of such ordered states by the real and by the imaginary parts of the coupling parameter.

We perform a study of a collective atomic recoil laser (CARL) that goes beyond the initial growth period. The study is based on a theory that treats both internal and external degrees of atomic freedom quantum mechanically but regards the laser light as a classical field obeying Maxwell’s equations. We introduce the concepts of momentum families and diffraction groups and organize the matter wave equations in terms of diffraction groups. The steady-state lasing conditions are discussed in connection with the probe gain in the recoil-induced resonances. The nontrivial steady states and the linear stability analysis of the steady states are both carried out by the method of two-dimensional continued fractions. Both stable and unstable nontrivial steady states are calculated and discussed in the context of regarding the CARL as multiwave mixing involving many modes of matter waves and two optical fields.